Finite Group DatabasebetaFinite Group Databasebeta| order | 10350 |
| isoclinism | isoclinic class of D23 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C25 · Schur multiplier (H2) = C3 |
| direct product | C32×C25×D23 |
| unambiguous semidirect product | C23⋊(C2×C32×C25) |
| Fitting, Hall | C32×C23×C25 ⋊ C2 |
| derived, Sylow | C23 ⋊ C2×C32×C25 |
| Hall | C23×C25 ⋊ C2×C32 |
| Hall | C32×C23 ⋊ C2×C25 |
72 conjugacy classes of subgroups.
2925 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×D23×D25, C3×D3×C25×D23, C3×D23×D75, … |
| maximal normal subgroup of | C32×D23×D25, C3×D3×C25×D23, C3×D23×D75, … |
| maximal quotient of | C32×C25×Dic23, C2×C32×C25×D23 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10350, 10);